I once saw an episode of Airline where a lady tried to bring a cooler of raw chicken on the plane. It was kind of funny. Luckily, they would not allow it. Your post reminded me of that. I wouldn't try to bring perishables on the plane.
A softsided cooler is apretty good idea. We tried this one time, though, and you have to restock the cooler with ice all the time, and they leak. Once we stayed at the Marriott. WE thought we'd have a fridge, so we boutgh milk and oj. Instead, they had a minibar. I was able to get teh milk in (by converting to empty water bottles) but the others were too big. WE used the spare sink and a towel to do a makeshift cooler. Worked better than the cooler, since it just drained down the drain. It was still a pain to keep it iced though.
We mostly want milk for our coffee. So here's one plan we use now, esp if we don't have a car. At most WDW resorts, the main bus stop is next to the resort gift shop. Most days, you can make a quick stop in the gift shop area and pick up a quart of milk (like the night before you want to drink it). You don't really have to go out of your way to do this. Milk in quarts costs more than buying it by the gallon at grocery stores, but it's less than buying it at the food courts in pints. You can also replenish it every day or so, so if you neglect your icing, the loss is small.
If I really need more milk in the room in the am, I send DH while I'm getting ready. It's good to give him a little task each morning to keep him from getting too restless.